Long-term deflection differs from short-term because

Sustained load causes creep and shrinkage, so it is larger and not recoverable

It is immediate and recoverable

It uses Ec = 5000 sqrt(fck) only

2082 Baisakh · 4 marks

Serviceability; short and long-term deflection

Short answer

The limit state of serviceability ensures satisfactory performance under working loads regarding deflection, cracking, vibration, and durability with γf = 1.0. Short-term deflection is immediate and elastic, using Ec = 5000√fck. Long-term deflection includes creep (effective modulus Ec/(1+θ), θ = 1.6) and shrinkage; total deflection is limited to span/250 and span/350 or 20 mm after partitions.

Define the limit state of serviceability. Differentiate between short-term and long-term deflection.

Limit state of serviceability is the state beyond which the structure, though safe against collapse, can no longer be used satisfactorily under service (working) loads because of excessive deflection, cracking or vibration, or because its durability is affected. IS 456 cl. 35 covers deflection, cracking, durability and vibration; deflection and cracking are checked in design with a partial safety factor $\gamma_f = 1.0$ on working loads.

Short-term and long-term deflection

Basis	Short-term (immediate) deflection	Long-term deflection
Cause	Occurs as soon as the load is applied; elastic behaviour of the (cracked) section	Sustained load causes creep, plus shrinkage of concrete
Modulus	$E_c = 5000\sqrt{f_{ck}}$ MPa	Effective modulus $E_{ce} = \dfrac{E_c}{1+\theta}$ ( $\theta$ = creep coefficient, 1.6 for loading at 28 days)
Occurs	Immediately; largely recovered when the load is removed	Slowly over months or years; not recovered
Value	Smaller	Larger (typically 2 to 3 times the short-term value)
Calculation	$a = \dfrac{5wl^4}{384E_cI_{eff}}$ (simply supported, UDL) with $I_{eff}$ from Annex C	$a_{total} = a_i + a_{cc} + a_{cs}$ : short-term deflection under all loads plus creep deflection under permanent loads plus shrinkage deflection (shrinkage strain 0.0003)

The total deflection due to all loads, including creep and shrinkage, should not exceed span/250, and the part occurring after construction of partitions and finishes should not exceed span/350 or 20 mm, whichever is less (IS 456 cl. 23.2).

✓ Answer checked by Claude Opus 5.5 (high effort)

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